Skip to main content

Flow net under sheet pile, discharge

Short answer

Steps: draw section to scale, identify boundaries (upstream/downstream surfaces equipotentials, pile faces and base flow lines), sketch 3-4 flow lines and equipotentials intersecting at right angles forming curvilinear squares, adjust by trial, count Nf and Nd. Discharge q = kH(Nf/Nd) per meter length, where H is net head loss.

Draw a flow net for the flow of water under a sheet pile wall. Write down the steps to draw this flow net and find the discharge, q, for this flow.

A sheet pile wall is driven into a pervious layer with an impervious base. The water level is higher upstream (head h1h_1) than downstream (h2h_2), so water flows under the pile tip.

  upstream ▽      |P|      ▽ downstream
  ----------------|P|----------------
   flow lines ~~> |P| ~~> curve under tip
  ================================== impervious

Steps to draw the flow net

  1. Draw the section to scale showing the sheet pile, soil surfaces and the impervious base.
  2. Note boundary conditions: upstream and downstream soil surfaces are equipotential lines; the sheet pile faces and the impervious base are flow lines.
  3. Draw 3 or 4 flow lines as smooth curves round the pile tip, perpendicular to the equipotentials.
  4. Draw equipotential lines, perpendicular to flow lines, so that the fields are squares.
  5. Adjust by trial and error until all fields are curvilinear squares.
  6. Count NfN_f and NdN_d.

Discharge

q=k H NfNdq = k\,H\,\frac{N_f}{N_d}

where H=h1−h2H = h_1 - h_2 is the net head loss, NfN_f the number of flow channels and NdN_d the number of equipotential drops. qq is in m³/s per metre length of the wall.

✓ Answer checked by Claude Opus 5.5 (high effort)

Related questions

All Soil Mechanics chapter 7 questions →